GAZA CITY (AFP) - Hamas Premier Ismail Haniya urged US President Barack Obama to correct the "mistakes" of his predecessor George W Bush, the Islamists said on Wednesday as the new US Middle East envoy held talks with Israeli Prime Minister in Jerusalem. "Given that you are a man who incarnates victory after a long struggle, we hope that you will rectify the errors of the previous administration," Haniya wrote in a letter. "Today we join you in the march towards change, change that will bring justice for all," he said. "Palestine is the door to the Muslim world," Haniya wrote, in an apparent reference to Obama's comments reaching out to the Muslim world following his inauguration. "Justice and freedom for Palestinians is the key that will open this door." The text of the letter was posted on a Hamas website, which did not say how the message, which also congratulated Obama on his inauguration, was sent to the US President. Talking to reporters after meeting Israeli Prime Minister Ehud Olmert in Jerusalem, US peace envoy Mitchell said it was vital to consolidate the ceasefire that ended the Gaza war. Mitchell met Israeli leaders after flying in from Egypt on the second leg of his maiden trip to the region under instructions from President Barack Obama to "engage vigorously" and resuscitate Israeli-Palestinian peace talks. "The prime minister and I discussed the critical importance to consolidate the ceasefire, including a cessation of hostilities, an end to smuggling and re-opening of the crossings based on 2005 agreements," he told reporters after meeting Olmert. Echoing comments made in Egypt after meeting President Hosni Mubarak, Mitchell promised that "the US will sustain an active commitment to reaching the goal of the two states living side by side in peace and security." Olmert, however, said Israel would open Gaza's borders - which it has kept sealed to all but essential humanitarian goods since the Islamists seized power there in June 2007 - if Hamas activists released a soldier they snatched in June 2006. "A permanent opening of the crossings will be linked to solving the issue of Gilad Shalit," a senior Israeli official quoted Olmert as telling the envoy. Senior Israeli officials, campaigning for the February 10 parliamentary election that the right-wing Opposition is widely expected to win, vowed that the Jewish state would strike back hard. "The army's reaction today was only operational. This was not the response to the killing of a soldier... Israel's response shall come," a senior government official quoted Olmert as saying. Defence Minister Ehud Barak cancelled his planned departure to the US on Wednesday because of the violence, a ministry official said. After talks with senior Israeli politicians and intelligence officials, Mitchell was to head to Ramallah in the occupied West Bank on Thursday for talks with Palestinian President Mahmud Abbas hit out at Israel ahead of a meeting with Mitchell. "Today we are convinced more than ever, especially after the aggression against Gaza, that Israel does not want peace and we are going to say so to all those who come to see us," he told reporters. He said his Palestinian Authority planned to go to the International Criminal Court over Israel's "atrocious crimes" in Gaza against the Palestinian people and also lashed out at his rivals in Hamas. The Islamists, who kicked pro-Abbas forces out of Gaza in June 2007, had "dragged an entire people" to war by refusing to renew an Egyptian-brokered six-month truce with Israel in December, Abbas said.